After you have mastered writing and graphing linear equations, it’s time to move on to writing and graphing linear inequalities. This starts out the same as graphing linear equations but quickly veers into new territory.

Just like graphing an equation, to graph a linear inequality, first manipulate the inequality so it’s in slope-intercept form, y = mx + b, by using opposite operations and isolating the y-value. But, different from equations, don’t forget to pay attention to any needed sign changes. If you multiply or divide by a negative number, remember to flip the sign. Once you have done that, using the y-intercept as your first point, use the slope to draw in additional points.

Before you draw a line to connect the dots, take a look at the inequality symbol, for less than or greater than – use a dotted line. For less than and equal to and greater than and equal to – use a solid line. Now shade in the solution set. As a rule, greater than is above the line, and less than is below the line but depending on the slope of the line, this may not be so obvious, so pick a test point and verify that the solution set works before you highlight the area in permanent ink. To see some real world uses of linear inequalities and learn some tips to make graphing easier, take a look at this fun video.